env_projectedtexture is a fickle mistress
So as a sanity check I built a room that only has an observation room (altered so that you can turn the lights off) and a floor button to control the lights. Sure enough, sometimes when I step on the button to turn the lights on, the env_projectedtexture doesn't activate. If I turn on 'developer 2' in the console it shows the TurnOn input being fired, but nothing happens.
Sometimes you get streaks where it works 5 or more times in a row, and then again sometimes you get multiple failures in a row.
I'm stumped. I don't know if it's a bug in the engine, a bug in Portal 2, or if I'm just missing something incredibly obvious. (I know which one is most likely.) 
My guess is that there's a mistake in the settings or something, but also try killing yourself/reloading the map. I've had trouble with it not working, then I've reloaded the map and it's worked fine.
I set the appearance to Normal (which has no variation) and now it works every time.